Three travelers arrive at a town where there are four hotels; in how many ways can they take up their rooms, each at a different hotel.
(A) 12 (B) 16 (C) 24
(D) 28 (E) 32

Question

Three travelers arrive at a town where there are four hotels; in how many ways can they take up their rooms, each at a different hotel.
(A) 12 (B) 16 (C) 24
(D) 28 (E) 32

wolf1728 · Answer

In order to think of this more neatly, think of the 4th traveler as an empty set.
So, the travelers can stay like this:
A B C D 
1 2 3 0 
1 2 0 3
1 0 2 3
1 0 3 2

In how many ways can the "four" travelers stay in the hotels.
You have to determine in how man ways can 4 things be arranged?
( 4! is a BIG hint)

anonymous · Answer

@wolf1728 thanks !!!